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  • Computable analogs of cardinal characteristics: Prediction and rearrangement
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-08-03
    Iván Ongay-Valverde; Paul Tveite

    There has recently been work by multiple groups in extracting the properties associated with cardinal invariants of the continuum and translating these properties into similar analogous combinatorial properties of computational oracles. Each property yields a highness notion in the Turing degrees. In this paper we study the highness notions that result from the translation of the evasion number and

    更新日期:2020-08-03
  • Towards the Entropy-Limit Conjecture
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-24
    Jürgen Landes; Soroush Rafiee Rad; Jon Williamson

    The maximum entropy principle is widely used to determine non-committal probabilities on a finite domain, subject to a set of constraints, but its application to continuous domains is notoriously problematic. This paper concerns an intermediate case, where the domain is a first-order predicate language. Two strategies have been put forward for applying the maximum entropy principle on such a domain:

    更新日期:2020-07-24
  • Preservation theorems for Namba forcing
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-23
    Osvaldo Guzmán; Michael Hrušák; Jindřich Zapletal

    We study preservation properties of Namba forcing on κ. We prove that if I is an ideal with a Borel base on ωω and κ>ω1 is a regular cardinal less than the uniformity number or bigger than the covering number of I, then the κ-Namba forcing preserves the covering of I. The situation at κ=ω1, also treated here, is more complex.

    更新日期:2020-07-23
  • Complexity of syntactical tree fragments of Independence-Friendly logic
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-17
    Fausto Barbero

    A dichotomy result of Sevenster (2014) completely classified the quantifier prefixes of regular Independence-Friendly (IF) logic according to the patterns of quantifier dependence they contain. On one hand, prefixes that contain “Henkin” or “signalling” patterns were shown to characterize fragments of IF logic that capture NP-complete problems; all the remaining prefixes were shown instead to be essentially

    更新日期:2020-07-17
  • Open core and small groups in dense pairs of topological structures
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-16
    Elias Baro; Amador Martin-Pizarro

    Dense pairs of geometric topological fields have tame open core, that is, every definable open subset in the pair is already definable in the reduct. We fix a minor gap in the published version of van den Dries's seminal work on dense pairs of o-minimal groups, and show that every definable unary function in a dense pair of geometric topological fields agrees with a definable function in the reduct

    更新日期:2020-07-16
  • Finitely generated groups are universal among finitely generated structures
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-03
    Matthew Harrison-Trainor; Meng-Che “Turbo” Ho

    Universality has been an important concept in computable structure theory. A class C of structures is universal if, informally, for any structure of any kind there is a structure in C with the same computability-theoretic properties as the given structure. Many classes such as graphs, groups, and fields are known to be universal. This paper is about the class of finitely generated groups. Because finitely

    更新日期:2020-07-13
  • |˜-divisibility of ultrafilters
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-07-03
    Boris Šobot

    We further investigate a divisibility relation on the set βN of ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions

    更新日期:2020-07-09
  • Filter-linkedness and its effect on preservation of cardinal characteristics
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-06-29
    Jörg Brendle; Miguel A. Cardona; Diego A. Mejía

    We introduce the property “F-linked” of subsets of posets for a given free filter F on the natural numbers, and define the properties “μ-F-linked” and “θ-F-Knaster” for posets in a natural way. We show that θ-F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families. Concerning iterations of such posets, we develop a general technique to construct θ-Fr-Knaster

    更新日期:2020-07-05
  • On equivalence relations generated by Cauchy sequences in countable metric spaces
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-06-25
    Longyun Ding; Kai Gu

    Let X be the set of all metrics on ω, and let Xcpt be the set of all metrics r on ω such that the completion of (ω,r) is compact. We define the Cauchy sequence equivalence relation Ecs on X as: rEcss iff the set of Cauchy sequences in (ω,r) is same as in (ω,s). We also denote Ecsc=Ecs↾Xcpt. We show that Ecs is a Π11-complete equivalence relation, while Ecsc is a Π30 equivalence relation. We also show

    更新日期:2020-07-02
  • The tree property at double successors of singular cardinals of uncountable cofinality with infinite gaps
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-06-18
    Mohammad Golshani; Alejandro Poveda

    Assume that κ and λ are respectively strong and weakly compact cardinals with λ>κ. Fix Θ≥λ a cardinal with cof(Θ)>κ and cof(δ)=δ<κ. Assuming the GCH≥κ holds, we construct a generic extension of the universe where κ is a strong limit cardinal, cof(κ)=δ, 2κ=Θ and TP(κ++) holds. This extends the main result of [4] for uncountable cofinalities.

    更新日期:2020-06-18
  • Proofs and surfaces
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-06-01
    Djordje Baralić; Pierre-Louis Curien; Marina Milićević; Jovana Obradović; Zoran Petrić; Mladen Zekić; Rade T. Živaljević

    A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Δ-complexes. The Euclidean and projective interpretations of the sequents are defined and a soundness result is proved. This system is decidable and its provable sequents deliver incidence results. A cyclic operad structure tied to this system is presented

    更新日期:2020-06-01
  • Structure and representation of semimodules over inclines
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-29
    Ruiqi Bai; Yichuan Yang

    An incline S is a commutative semiring where r+1=1 for any r∈S. We note that the ideal lattice of an S-semimodule is naturally an S-semimodule and so is its congruence lattice when S is transitive. We prove that the categories of complete S-semimodules, together with dual functor, internal hom and tensor product, is a ⋆-autonomous category. We define the locally and globally maximal congruences which

    更新日期:2020-05-29
  • The FAN principle and weak König's lemma in herbrandized second-order arithmetic
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-28
    Fernando Ferreira

    We introduce a herbrandized functional interpretation of a first-order semi-intuitionistic extension of Heyting Arithmetic and study its main properties. We then extend the interpretation to a certain system of second-order arithmetic which includes a (classically false) formulation of the FAN principle and weak König's lemma. It is shown that any first-order formula provable in this system is classically

    更新日期:2020-05-28
  • Join-Completions of Partially Ordered Algebras
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-23
    José Gil-Férez; Luca Spada; Constantine Tsinakis; Hongjun Zhou

    We present a systematic study of join-extensions and join-completions of partially ordered algebras, which naturally leads to a refined and simplified treatment of fundamental results and constructions in the theory of ordered structures ranging from properties of the Dedekind–MacNeille completion to the proof of the finite embeddability property for a number of varieties of lattice-ordered algebras

    更新日期:2020-05-23
  • Ultrafilters, finite coproducts and locally connected classifying toposes
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-19
    Richard Garner

    We prove a single category-theoretic result encapsulating the notions of ultrafilters, ultrapower, ultraproduct, tensor product of ultrafilters, the Rudin–Kiesler partial ordering on ultrafilters, and Blass's category of ultrafilters UF. The result in its most basic form states that the category FC(Set,Set) of finite-coproduct-preserving endofunctors of Set is equivalent to the presheaf category [UF

    更新日期:2020-05-19
  • Polish metric spaces with fixed distance set
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-19
    Riccardo Camerlo; Alberto Marcone; Luca Motto Ros

    We study Polish spaces for which a set of possible distances A⊆R+ is fixed in advance. We determine, depending on the properties of A, the complexity of the collection of all Polish metric spaces with distances in A, obtaining also example of sets in some Wadge classes where not many natural examples are known. Moreover we describe the properties that A must have in order that all Polish spaces with

    更新日期:2020-05-19
  • Diagonal supercompact Radin forcing
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-18
    Omer Ben-Neria; Chris Lambie-Hanson; Spencer Unger

    Motivated by the goal of constructing a model in which there are no κ-Aronszajn trees for any regular κ>ℵ1, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square fail.

    更新日期:2020-05-18
  • Rules with parameters in modal logic II
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-15
    Emil Jeřábek

    We analyze the computational complexity of admissibility and unifiability with parameters in transitive modal logics. The class of cluster-extensible (clx) logics was introduced in the first part of this series of papers [8]. We completely classify the complexity of unifiability or inadmissibility in any clx logic as being complete for one of Σ2exp, NEXP, coNEXP, PSPACE, or Π2p. In addition to the

    更新日期:2020-05-15
  • Modal extension of ideal paraconsistent four-valued logic and its subsystem
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-15
    Norihiro Kamide; Yoni Zohar

    This study aims to introduce a modal extension M4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic 4CC as a Gentzen-type sequent calculus and prove the Kripke-completeness and cut-elimination theorems for M4CC. The logic M4CC is also shown to be decidable and embeddable into the normal modal logic S4. Furthermore, a subsystem of M4CC, which has some characteristic properties

    更新日期:2020-05-15
  • Epimorphism surjectivity in varieties of Heyting algebras
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-13
    T. Moraschini; J.J. Wannenburg

    It was shown recently that epimorphisms need not be surjective in a variety K of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by the Rieger-Nishimura lattice, and all of its (locally finite) subvarieties that contain the original counter-example K. It is known that, whenever a variety

    更新日期:2020-05-13
  • Perfect tree forcings for singular cardinals
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-13
    Natasha Dobrinen; Dan Hathaway; Karel Prikry

    We investigate forcing properties of perfect tree forcings defined by Prikry to answer a question of Solovay in the late 1960's regarding first failures of distributivity. Given a strictly increasing sequence of regular cardinals 〈κn:n<ω〉, Prikry defined the forcing P of all perfect subtrees of ∏n<ωκn, and proved that for κ=supn<ω⁡κn, assuming the necessary cardinal arithmetic, the Boolean completion

    更新日期:2020-05-13
  • A premouse inheriting strong cardinals from V
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-12
    Farmer Schlutzenberg

    We identify a premouse inner model L[E], such that for any coarsely iterable background universe R modelling ZFC, L[E]R is a proper class premouse of R inheriting all strong and Woodin cardinals from R. For each ordinal α, L[E]R|α is (ω,α)-iterable, via iteration trees which lift to coarse iteration trees on R. We prove that (k+1)-condensation follows from (k+1)-solidity together with (k,ω1+1)-iterability

    更新日期:2020-05-12
  • Silver type theorems for collapses
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-11
    Moti Gitik

    Let κ be a cardinal of cofinality ω1 witnessed by a club of cardinals 〈κα|α<ω1〉. We study Silver's type effects of collapsing of κα+'s on κ+. A model in which κα+'s (and also κ+) are collapsed on a stationary co-stationary set is constructed.

    更新日期:2020-05-11
  • Some constructions of ultrafilters over a measurable cardinal
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-06
    Moti Gitik

    Some non-normal κ-complete ultrafilters over a measurable κ with special properties are constructed. Questions by A. Kanamori [4] about infinite Rudin-Frolik sequences, discreteness and products are answered.

    更新日期:2020-05-06
  • Algebraically closed structures in positive logic
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-06
    Mohammed Belkasmi

    In this paper we extend of the notion of algebraically closed given in the case of groups and skew fields to an arbitrary h-inductive theory. The main subject of this paper is the study of the notion of positive algebraic closedness and its relationship with the notion of positive closedness and the amalgamation property.

    更新日期:2020-05-06
  • Computability of pseudo-cubes
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-05-04
    Marko Horvat; Zvonko Iljazović; Bojan Pažek

    We examine topological pairs (Δ,Σ) which have computable type: if X is a computable topological space and f:Δ→X a topological embedding such that f(Δ) and f(Σ) are semicomputable sets in X, then f(Δ) is a computable set in X. It it known that (D,W) has computable type, where D is the Warsaw disc and W is the Warsaw circle. In this paper we identify a class of topological pairs which are similar to

    更新日期:2020-05-04
  • A forcing axiom for a non-special Aronszajn tree
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-04-30
    John Krueger

    Suppose that T⁎ is an ω1-Aronszajn tree with no stationary antichain. We introduce a forcing axiom PFA(T⁎) for proper forcings which preserve these properties of T⁎. We prove that PFA(T⁎) implies many of the strong consequences of PFA, such as the failure of very weak club guessing, that all of the cardinal characteristics of the continuum are greater than ω1, and the P-ideal dichotomy. On the other

    更新日期:2020-04-30
  • The theory of ceers computes true arithmetic
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-04-10
    Uri Andrews; Noah Schweber; Andrea Sorbi

    We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the structure comprised of the light ceers. We also show the same for the structure of I-degrees in the dark, light, or complete structure. In each case, we show that

    更新日期:2020-04-10
  • A classification of the cofinal structures of precompacta
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-04-08
    Aviv Eshed; M. Vicenta Ferrer; Salvador Hernández; Piotr Szewczak; Boaz Tsaban

    We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general complete metric spaces. Using this classification, we classify the cofinal structure of local bases in the groups C(X,R) of continuous real-valued functions on complete metric spaces X, with respect to the compact-open topology

    更新日期:2020-04-08
  • On expansions of (Z,+,0)
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-03-25
    Quentin Lambotte; Françoise Point

    Call a (strictly increasing) sequence (rn) of natural numbers regular if it satisfies the following condition: rn+1/rn→θ∈R>1∪{∞} and, if θ is algebraic, then (rn) satisfies a linear recurrence relation whose characteristic polynomial is the minimal polynomial of θ. Our main result states that (Z,+,0,R) is superstable whenever R is enumerated by a regular sequence. We give two proofs of this result

    更新日期:2020-03-25
  • Expansions of real closed fields that introduce no new smooth functions
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-03-23
    Pantelis E. Eleftheriou; Alex Savatovsky

    We prove the following theorem: let R˜ be an expansion of the real field R‾, such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a “semialgebraic chunk”. Then every definable smooth function f:X⊆Rn→R with open semialgebraic domain is semialgebraic. Conditions (I) and (II) hold for various d-minimal expansions R˜=〈R‾,P〉 of the real field, such as when

    更新日期:2020-03-23
  • The density zero ideal and the splitting number
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-03-19
    Dilip Raghavan

    The main result of this paper is an improvement of the upper bound on the cardinal invariant cov⁎(Z0) that was discovered in [11]. Here Z0 is the ideal of subsets of the set of natural numbers that have asymptotic density zero. This improved upper bound is also dualized to get a better lower bound on the cardinal non⁎(Z0). En route some variations on the splitting number are introduced and several

    更新日期:2020-03-19
  • Some lower bounds on Shelah rank in the free group
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-03-12
    Javier de la Nuez González; Chloé Perin; Rizos Sklinos

    We give some lower bounds on the Shelah rank of varieties in the free group whose coordinate groups are hyperbolic towers.

    更新日期:2020-03-12
  • M-separable spaces of functions are productive in the Miller model
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-03-10
    Dušan Repovš; Lyubomyr Zdomskyy

    We prove that in the Miller model, every M-separable space of the form Cp(X), where X is metrizable and separable, is productively M-separable, i.e., Cp(X)×Y is M-separable for every countable M-separable Y.

    更新日期:2020-03-10
  • Definable groups in models of Presburger Arithmetic
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-03-09
    Alf Onshuus; Mariana Vicaría

    This paper is devoted to understand groups definable in Presburger Arithmetic. We prove the following theorems: Theorem 1. Every group definable in a model of Presburger Arithmetic is abelian-by-finite. Theorem 2. Every bounded abelian group definable in a model (Z,+,<) of Presburger Arithmetic is definably isomorphic to (Z,+)n mod out by a lattice.

    更新日期:2020-03-09
  • Expander construction in VNC1
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-03-04
    Sam Buss; Valentine Kabanets; Antonina Kolokolova; Michal Koucký

    We give a combinatorial analysis (using edge expansion) of a variant of the iterative expander construction due to Reingold, Vadhan, and Wigderson [44], and show that this analysis can be formalized in the bounded arithmetic system VNC1 (corresponding to the “NC1 reasoning”). As a corollary, we prove the assumption made by Jeřábek [28] that a construction of certain bipartite expander graphs can be

    更新日期:2020-03-04
  • Univalent polymorphism
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-02-21
    Benno van den Berg

    We show that Martin Hyland's effective topos can be exhibited as the homotopy category of a path category EFF. Path categories are categories of fibrant objects in the sense of Brown satisfying two additional properties and as such provide a context in which one can interpret many notions from homotopy theory and Homotopy Type Theory. Within the path category EFF one can identify a class of discrete

    更新日期:2020-02-21
  • Characterizations of the weakly compact ideal on Pκλ
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-02-19
    Brent Cody

    Hellsten [15] gave a characterization of Πn1-indescribable subsets of a Πn1-indescribable cardinal in terms of a natural filter base: when κ is a Πn1-indescribable cardinal, a set S⊆κ is Πn1-indescribable if and only if S∩C≠∅ for every n-club C⊆κ. We generalize Hellsten's characterization to Πn1-indescribable subsets of Pκλ, which were first defined by Baumgartner. First we show that under reasonable

    更新日期:2020-02-19
  • Herbrand's theorem as higher order recursion
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-02-19
    Bahareh Afshari; Stefan Hetzl; Graham E. Leigh

    This article examines the computational content of the classical Gentzen sequent calculus. There are a number of well-known methods that extract computational content from first-order logic but applying these to the sequent calculus involves first translating proofs into other formalisms, Hilbert calculi or Natural Deduction for example. A direct approach which mirrors the symmetry inherent in sequent

    更新日期:2020-02-19
  • Bilattice logic of epistemic actions and knowledge
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-02-14
    Zeinab Bakhtiari; Hans van Ditmarsch; Umberto Rivieccio

    Baltag, Moss, and Solecki proposed an expansion of classical modal logic, called logic of epistemic actions and knowledge (EAK), in which one can reason about knowledge and change of knowledge. Kurz and Palmigiano showed how duality theory provides a flexible framework for modeling such epistemic changes, allowing one to develop dynamic epistemic logics on a weaker propositional basis than classical

    更新日期:2020-02-14
  • Embeddings between well-orderings: Computability-theoretic reductions
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2020-02-11
    Jun Le Goh

    We study the computational content of various theorems with reverse mathematical strength around Arithmetical Transfinite Recursion (ATR0) from the point of view of computability-theoretic reducibilities, in particular Weihrauch reducibility. Our main result states that it is equally hard to construct an embedding between two given well-orderings, as it is to construct a Turing jump hierarchy on a

    更新日期:2020-02-11
  • Turing reducibility in the fine hierarchy
    Ann. Pure Appl. Logic (IF 0.752) Pub Date : 2019-12-13
    Alexander G. Melnikov; Victor L. Selivanov; Mars M. Yamaleev

    In the late 1980s, Selivanov used typed Boolean combinations of arithmetical sets to extend the Ershov hierarchy beyond Δ20 sets. Similar to the Ershov hierarchy, Selivanov's fine hierarchy {Σγ}γ<ε0 proceeds through transfinite levels below ε0 to cover all arithmetical sets. In this paper we use a 0‴ construction to show that the Σ30 Turing degrees are properly contained in the Σωω+2 Turing degrees

    更新日期:2019-12-13
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